We are developing mathematical and computational models of mechanisms of T cell differentiation and homeostasis. In healthy individuals, a balance between cell death, proliferation and differentiation into T cell subtypes with certain effector functions and proliferative potential maintains a sufficient population of recirculating and peripheral effector cells. In HIV / SIV infected individuals / Rhesus macaques, damage to the lymphoid system and the initial viral killing of peripheral T cells especially in the mucosal tissues lead to an immediate deficit of effector cells in the periphery which persists even after treatment with anti-retroviral drugs because the restorative capacity of the central (recirculating) T cells is destroyed. We are trying to answer the following questions: What leads to a destabilization of T cell proliferation and differentiation in HIV / SIV infection? How does this manifest itself as altered proliferation/death/differentiation rates of T cells? What are the differences between CD4 and CD8 cells? To try to answer these questions we develop mathematical models describing the division, death and differentiation of T cells. These models can be represented as sets of coupled linear ordinary differential equations for the dynamics of the sizes of the different cell populations. We then try to determine which model is capable of most precisely matching the experimental data through parameter optimizations (fitting).